Modeling competitive evolution of multiple languages

Increasing evidence demonstrates that in many places language coexistence has become ubiquitous and essential for supporting language and cultural diversity and associated with its financial and economic benefits. The competitive evolution among multiple languages determines the evolution outcome, either coexistence, decline, or extinction. Here, we extend the Abrams-Strogatz model of language competition to multiple languages and then validate it by analyzing the behavioral transitions of language usage over the recent several decades in Singapore and Hong Kong. In each case, we estimate from data the model parameters that measure each language utility for its speakers and the strength of two biases, the majority preference for their language, and the minority aversion to it. The values of these two biases decide which language is the fastest growing in the competition and what would be the stable state of the system. We also study the system convergence time to stable states and discover the existence of tipping points with multiple attractors. Moreover, the critical slowdown of convergence to the stable fractions of language users appears near and peaks at the tipping points, signaling when the system approaches them. Our analysis furthers our understanding of multiple language evolution and the role of tipping points in behavioral transitions. These insights may help to protect languages from extinction and retain the language and cultural diversity.Comment: 13 pages, 6 figure

True Nonlinear Dynamics from Incomplete Networks

We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^*$. We develop fundamental tools to learn the true steady-state of a small part of the network, without knowing the full network. A naive approach and the current state-of-the-art is to follow the dynamics of the observed partial network to local equilibrium. This dramatically fails to extract the true steady state. We use a mean-field approach to map the dynamics of the unseen part of the network to a single node, which allows us to recover accurate estimates of steady-state on as few as 5 observed vertices in domains ranging from ecology to social networks to gene regulation. Incomplete networks are the norm in practice, and we offer new ways to think about nonlinear dynamics when only sparse information is available.Comment: AAAI 2020, 9 pages, 5 figure

FIELD TEST ON THE COOPERATION OF NSM STRENGTHENING AND EXTERNAL TENDON RETROFITTING TECHNIQUE

In this paper, post-tension and steel plate near-surface mounted (NSM) strengthening systems are proposed to strengthen deteriorated and cracked large box girder rigid frame bridge without altering appearance and dimension of the bridge. The reinforcement method mainly improves the bearing capacity through external prestressed tendons, and bonding steel plate can enhance the shear resistance of the bridge. The main purpose is to study the structural mechanical properties before and after the reinforcement of rigid frame bridges. Take a 540m rigid frame box girder bridge as an example. The static load test of the bridge before and after reinforcement is carried out. The deflection and strain of the middle cross section of the span are measured in the static test. A finite element analysis model was also developed and verified static loading test data. The results show that structural bearing capacity and performance of the bridge were enhanced with the post-tension and NSM strengthening systems cooperatively

Target control of complex networks

Controlling large natural and technological networks is an outstanding challenge. It is typically neither feasible nor necessary to control the entire network, prompting us to explore target control: the efficient control of a preselected subset of nodes. We show that the structural controllability approach used for full control overestimates the minimum number of driver nodes needed for target control. Here we develop an alternate ‘k-walk’ theory for directed tree networks, and we rigorously prove that one node can control a set of target nodes if the path length to each target node is unique. For more general cases, we develop a greedy algorithm to approximate the minimum set of driver nodes sufficient for target control. We find that degree heterogeneous networks are target controllable with higher efficiency than homogeneous networks and that the structure of many real-world networks are suitable for efficient target control